Last trip (5 years ago in May), I was 4 months pregnant, and my legs started swelling by 9am every morning BEFORE we left for FL. I have always worn Birkenstocks at Disney - never had a blister. If you can stand sneakers, that's probably best, but since you're a flip-flop wearer, you'll probably be most comfortable in GOOD SUPPORTIVE sandals (but not flip-flops). My current favorite sandals are river sandals used primarily for kayaking. The soles are super cushy, the straps are quick-dry webbing, and they're adjustable in every direction. They're Tevas (not the standard style - one of the river styles), but lots of companies make similar sandals. Whatever you choose, make sure you break them in really well!
I would avoid flip-flops due to the loosening of your joints. Your hips may not be working "normally" while you're there, and flip-flops won't help you catch your footing. And could just possibly cause some damage (sprained ankle?)